Asymptotic behavior of solutions to higher order nonlinear delay differential equations
In this article, we study the oscillation and asymptotic behavior of solutions to the nonlinear delay differential equation $$ x^{(n+3)}(t)+p(t)x^{(n)}(t)+q(t)f(x(g(t)))=0. $$ By using a generalized Riccati transformation and an integral averaging technique, we establish sufficient condition...
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| Format: | Article |
| Language: | English |
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Texas State University
2014-09-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/186/abstr.html |
| Summary: | In this article, we study the oscillation and asymptotic behavior of solutions
to the nonlinear delay differential equation
$$
x^{(n+3)}(t)+p(t)x^{(n)}(t)+q(t)f(x(g(t)))=0.
$$
By using a generalized Riccati transformation and an integral averaging technique,
we establish sufficient conditions for all solutions to oscillate, or to
converge to zero. Especially when the delay has the form $g(t)=at-\tau$,
we provide two convenient oscillatory criteria.
Some examples are given to illustrate our results. |
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| ISSN: | 1072-6691 |